Magnetic Force

Introduction

Magnetism has its applications in multiple fields. The force behind magnetism is ideally termed the Magnetic Force. It is a resultant of the electromagnetic force and is present only in charged conductors. Further, interacting magnetic fields produce this force of attraction of repulsion. The magnetic repulsion or magnetic attraction is calculated and determined by various laws in physics.

It is easy to calculate the force observed between two charged particles and the magnetic effects on a current-carrying conductor. The different laws like Lorentz Force Law and Right-Hand rule help determine the magnitude and direction of Magnetic Force.

Magnetic Force

The force caused by the movement of charges, which is one of the fundamental forces in nature, is Magnetic Force. Hence, any two objects having charge and moving in the opposite direction have a magnetic repulsive force between them. The force for the two objects having charge and moving in the same direction is attractive. Any two interacting magnetic fields cause this force.

Hence, moving charges and magnetism result in a force responsible for the attraction or repulsion of magnets to all objects. Further, the action of electric motors is due to the seamless coordination of magnetic and electric forces. Any moving electric charges possess magnetic and electric fields.

Calculation of Magnetic Force

The force between two charged particles moving with respect to each other depends on the quantity of charge and amount of motion between the two charges. It further depends on the distance between the charges at any point. The direction of the magnetic resultant force further depends on the relative directions of the motion of charge to each other. This is because this force resulting due to the magnetic field is a vector quantity.

Hence, while calculating the magnetic force, it is important to know certain quantities like the amount of charge on the object, the velocity of the movement of charge and the amount of the uniform magnetic field. Hence, a relation between all these quantities helps determine the magnitude and direction of the magnetic forces.

Lorentz Force Law

The magnetic force is called Lorentz force. Hence, Lorentz Force Law determines the relation between electric and magnetic fields. The equation of this law is:

F = qE + q(v × B).

It is the force exerted on the charged particle q moving at a velocity v in an electric field E and magnetic field B. Hence, the combined force is called Lorentz force, named after the Dutch physicist Hendrik A Lorentz.

The electric force is related to the amount of electric field and the amount of the charge. The magnetic component of Lorentz’s force is related to the quantity of charge, the velocity of electric charge and the amount of the magnetic field. The vector product of v and B helps consider the direction of the force. Hence, the magnitude of force equals the qvBsin(theta).

Hence, a charged particle moving in a magnetic field experiences a resultant force. If the value of theta is less than 90 degrees, the charged particle will follow a circular trajectory with radius r= mv/qB

If the value of theta is zero, the charged particle will continue to follow a straight path without getting deflected along the magnetic field lines.

Direction of the Magnetic Force

Since it is a vector quantity, it is important to consider the direction of this force. It further helps reveal the sign of charge carriers in the conductor. If current flows from the right to left in the conductor, it is due to the positive charge carriers moving from right to left or the negative charge carriers moving from left to right.

If the conductor is placed in the magnetic field perpendicular to the current, the magnetic field on both types of charge carriers is in the same direction. It results in a potential difference between conductor sides and is determined by the Hall effect.

Right-Hand Rule

The right-hand rule determines the direction of the magnetic force experienced by the conductor carrying current.

Whenever a charge moves in the magnetic field, it observes magnetic force. Lorentz law states that this force, F is:

F= qvBsin (θ)

Where q is the charge

v is the velocity

B is the magnetic field

θ is the angle between B and v.

The plane thus formed by the velocity v of the charged particle and direction of the magnetic field is at a right angle to the force experienced by the conductor. This right-angle validates the use of the right-hand rule to determine the orientation of the force.

It states that if the thumb denotes the direction of the velocity of charge and the first finger is in the direction of the magnetic field, the middle finger denotes the direction of the Magnetic Force.

Magnetic Force on a Current-carrying Conductor

The force on a current-carrying conductor in a magnetic field is used to convert electric energy to work. The charges can’t simply escape a conductor, and hence the magnetic effects on the charge in a current-carrying conductor are transmitted to the conductor itself. The resultant magnetic force can be determined by considering the sum of individual magnetic forces on multiple charges.

Considering the magnetic force on the current-carrying conductor to be F, it is

F= (nqAvd)lBsin (θ) or F= IlBsin (θ)

As I = nqAvd

Here, vd is the drift velocity,

B is the magnetic field,

q is the charge,

n is the number of charge carriers,

A is the cross-sectional area of the conductor,

θ is the angle between the magnetic field and current.

Conclusion

So, the magnetic force is one of the two fundamental forces on moving charges. The two different objects have a charge in the same direction of motion and magnetic attraction force between them, while the different objects having charges moving in the opposite direction have repulsive forces.

Lorentz’s law determines the relation between magnetic force, current and magnetic field. Since it is a vector quantity, its direction is determined by the right-hand thumb or slap rule. It is easy to calculate the magnitude and direction of this force on the moving conductor or current-carrying conductor exposed to the magnetic field. It has multiple applications like the attraction of magnets for iron, the action of electric motors, etc.